A165966 Triangular numbers that are sums of twin prime pairs.

36, 120, 276, 300, 2556, 3240, 5460, 8256, 12720, 23436, 26796, 34980, 41616, 46056, 56616, 59340, 103740, 122760, 139656, 147696, 157080, 185136, 195000, 231540, 277140, 333336, 353220, 386760, 401856, 516636, 609960, 860016, 1001820

Offset

1,1

Comments

All terms are multiples of 12.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

a(n) = A105174(n)*(A105174(n) + 1)/2.

Example

36 = 8*9/2 is a term since it is triangular and the sum of the twin primes 17 and 19.
120 = 15*16/2 is a term since it is triangular and the sum of the twin primes 59 and 61.

Mathematica

tri[n_] := n*(n+1)/2; Select[tri /@ Range[10^3], And @@ PrimeQ[#/2 + {-1, 1}] &] (* Amiram Eldar, Dec 27 2019 *)

Prog

(PARI) lista(nn) = {for (n = 1, nn, trg = n*(n+1)/2; if (!(trg % 2) && isprime(trg/2-1) && isprime(trg/2+1), print1(trg, ", ")); ); } \\ Michel Marcus, Oct 16 2013

Crossrefs

Subsequence of A111163 and of A054735.

Cf. A000217, A001359, A105174.

Sequence in context: A350500 A287861 A242356 * A307939 A254146 A173420

Adjacent sequences: A165963 A165964 A165965 * A165967 A165968 A165969

Keyword

nonn

Author

Zak Seidov, Oct 01 2009

Status

approved